(3) A company manufacturing laundry sinks has fixed costs of $100 per day but has totalcosts of $2,500 per day when producing 15 sinks. The company has a daily demand functionof q == 360p, where q is the number if laundry sinks demanded and p is te price ofa laundry sink.(a) If we assume that the total cost per day is linearly related to the amount of sinksproduced in a day, derive the total cost function of the company?(b) Find a function for the average cost of this company.(c) If production increases continuously, what is likely to be the average cost per sink?(d) How many laundry sinks will the company need to produce in order to maximise it's profits?(e) What is the maximum profit?Problem Set B1. The demand function for a good is given by the equation Pcost function is TC = dQ² + eQ+ f, where a, b, d, e and f are positive constants.= a – bQ while the total (1) The following is known about three numbers: Three times the first number plus the secondnumber plus twice the third number is 5. If 3 times the second number is subtracted fromthe sum of the first number and 3 times the third number, the result is 2. If the third numberis subtracted from 2 times the first number and 3 times the second number, the result is 1.(a) Write a system of equations to match the description of the information given.(b) Find the numbers using Cramer's Rule.(2) A certain brand of tea bags comes in packages of 5, 10, and 20 sachets, costing$5, $9, and $15 per package, respectively.A store sold 16 packages containing a total of 165 sachets and took in $140.27 / 40II(a) Write a system of equations to match the description of the information given.(b) Determine how many packages of each type were sold using the Inverse Method.

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Answered: (1) The following is known about three…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 16EQ

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(3) A company manufacturing laundry sinks has fixed costs of $100 per day but has total
costs of $2,500 per day when producing 15 sinks. The company has a daily demand function
of q =
= 360
p, where q is the number if laundry sinks demanded and p is te price of
a laundry sink.
(a) If we assume that the total cost per day is linearly related to the amount of sinks
produced in a day, derive the total cost function of the company?
(b) Find a function for the average cost of this company.
(c) If production increases continuously, what is likely to be the average cost per sink?
(d) How many laundry sinks will the company need to produce in order to maximise it's profits?
(e) What is the maximum profit?
Problem Set B
1. The demand function for a good is given by the equation P
cost function is TC = dQ² + eQ+ f, where a, b, d, e and f are positive constants.
= a – bQ while the total

Transcribed Image Text:(1) The following is known about three numbers: Three times the first number plus the second number plus twice the third number is 5. If 3 times the second number is subtracted from the sum of the first number and 3 times the third number, the result is 2. If the third number is subtracted from 2 times the first number and 3 times the second number, the result is 1. (a) Write a system of equations to match the description of the information given. (b) Find the numbers using Cramer's Rule. (2) A certain brand of tea bags comes in packages of 5, 10, and 20 sachets, costing $5, $9, and $15 per package, respectively. A store sold 16 packages containing a total of 165 sachets and took in $140. 27 / 40 II (a) Write a system of equations to match the description of the information given. (b) Determine how many packages of each type were sold using the Inverse Method.

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